The name came from the 1889 play Fédora, written for the great French tragedienne Sarah Bernhardt, in which she played a Princess of the same name and sported a hat of this design. As a result, it was initially a woman’s fashion item, particularly popular in the demimonde of 1920s Weimar Berlin.
It found its greatest favour with men however (especially in an era of open-top cars) and is, as Jon demonstrates, often associated with the Prohibition era. Orthodox Jewish men adopted it in the early 20th century, and remain staunch wearers to this day.
Aside from young urban Bohemians and assorted retro enthusiasts, anyone sporting such a hat in the 21st century – especially in the provinces – would indeed seem “eccentric”.